Weights were recorded for all nurses at a particular hospital, the mean weight for an individual nurse was 135 lbs. with a standard deviation of 15. if 19 nurses are selected at random, find the probability that the mean weight is between 125 and 130 lbs

Given:
population mean, μ =135
population standard deviation, σ = 15
sample size, n = 19

Assume a large population, say > 100,
we can reasonably assume a normal distribution, and a relatively small sample.
The use of the generally simpler formula is justified.

Estimate of sample mean


Estimate of sample standard deviation

  to 5 decimal places.

Thus, using the normal probability table,






Therefore 
The probability that the mean weight is between 125 and 130 lbs 
P(125<X<130)=0.0731166-0.0018308
=0.0712858